Quantum Imaging via Kurtosis-Difference Weighted Covariance on 2D Camera

Abstract: Camera-based quantum imaging detects spatially correlated photon pairs from spontaneous parametric down-conversion (SPDC). Conventional covariance methods typically require tens of thousands of frames to extract weak correlations from noise. While thick crystals can increase photon flux, they generate photon pairs from multiple emission positions within the crystal, producing multiple correlation centers with complex pairing geometries. In addition, conventional covariance methods assume a single pre-selected correlation center and cannot fully exploit these distributed correlations. We demonstrate that kurtosis difference, a fourth-order statistic measuring tail similarity, effectively discriminates correlated pixel pairs even when correlation coefficients remain low. Weighting covariance by an exponential function of absolute kurtosis difference can select symmetric pixels while preserving true coincidences. This kurtosis weighting automatically identifies correlated pairs within a broad search region and accommodates multiple pairing geometries without requiring precise correlation center calibration. At 5000 frames, our method yields a contrast-to-noise ratio (CNR) exceeding 7, whereas standard covariance remains below 2. Compared with standard covariance, the method reduces the acquisition time by 40-fold and could enable practical quantum imaging in sparse correlated-photon regimes.